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1 year ago

given the following information, determine which lines, if any, are parallel. state the converse that justifies your answer.

1 answer:

3 0

From the information in the diagram found in a similar question online (please see attached drawing), the parallel lines are;

w||z
x||y
x||y
w||z
w||z
x||y
x||y
w||z
x||y
w||z

<h3>What are the relationships between angles formed by parallel lines?</h3>

Parallel lines are lines that do not meet, when extended indefinitely.

The possible information given as obtained from a similar question posted online are;

1. ‹1 is congruent to ‹5

2. ‹7 is congruent to ‹9

3. m‹8 + m‹9 = 180°

4. ‹16 is congruent to ‹14

5. m‹1 + m‹4 = 180°

6. ‹3 is congruent to ‹13

7. ‹2 is congruent to ‹10

8. ‹11 is congruent to ‹15

9. m‹4 + m‹13 = 180°

10. ‹8 is congruent to ‹6

1. Given that ‹1 is congruent to ‹5 where ‹1 and ‹5 are alternate exterior angles, we have that line w is parallel to line z

w||z

Theorem (converse); Alternate exterior angles formed by two parallel lines having a common transversal are congruent.

2. ‹7 and ‹9 are alternate interior angles.

Given that ‹7 is congruent to ‹9, therefore;

Line x is parallel to line y

x||y

Theorem (converse); Alternate interior angles formed by two parallel lines having a common transversal are congruent.

3. Given that m‹8 + m‹9 = 180°, therefore;

‹8 and ‹9 are supplementary angles, formed between lines x and y.

‹8 and ‹9 are also consecutive interior angles.

Theorem (converse); Consecutive interior angles formed between parallel lines are supplementary.

Therefore;

x||y

4. ‹16 and ‹14 are corresponding angles formed by lines w and z.

Theorem (converse); Corresponding angles formed by parallel lines are congruent.

Given ‹16 congruent to ‹14, we have;

w||z

5. m‹1 and m‹4 are consecutive exterior angles formed by lines w and z.

Theorem (converse); Consecutive exterior angles formed by two parallel lines are supplementary.

Given that m‹1 + m‹4 = 180°, we have;

w||z

6. ‹3 and ‹13 are alternate exterior angles formed by lines x and y.

Theorem (converse); Alternate exterior angles formed by parallel lines are congruent.

Given that ‹3 congruent to ‹13, we have;

x||y

7. ‹2 and ‹10 are corresponding angles formed by lines x and y

Given that ‹2 congruent to ‹10, therefore;

x||y

8. ‹11 and ‹15 are alternate interior angles formed by lines w and z.

‹11 is congruent to ‹15, therefore;

w||z

9. ‹4 and ‹13 are consecutive exterior angles formed by lines x and y

m‹4 + m‹13 = 180°, therefore;

x||y

10. ‹8 and ‹6 are corresponding angles formed by lines w and z.

‹8 is congruent to ‹6, therefore;

w||z

Learn more about angles formed by parallel lines that have a common transversal here:

brainly.com/question/24607467

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3 years ago

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4 years ago

76 decreased by twice a number in an algebraic expression

soldier1979 [14.2K]

Answer is 76 - 2x
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3 years ago

Miss Berk has 8 pairs of pajama pants and 3 pairs of slippers. Three pairs of the pajama pants are Harry Potter themed and one p

shusha [124]

The probability that both items will be Harry Potter themed is 1/8.

Step-by-step explanation:

Total Number of pajama pants n(P) =8

Total number of slippers n(S)= 3

Number of Harry Potter themed Pajama pants n(H.P)=3

Number of Harry Potter themed slippers n(H.S)=1

We have to determine the probability of selecting pants and slippers that are both Harry Potter themed.

If two events A and B are independent, then the probability of A and B is given by

P(A and B)=P(A)*P(B)

Here the events selecting Harry potter themed pants and selecting harry Potter themed slippers are independent.

$P(Harry\ Potter\ pants)=\frac{n(H.P)}{n(P)}$

$=\frac{3}{8}$

$P(Harry\ Potter\ slippers)=\frac{n(H.S)}{n(S)} \\ =1/3$

$P(Harry\ Potter\ pants\ and\ Harry\ Potter\ slippers)=P(Harry Potter pants)\times P(Harry potter slippers)$

$=\frac{3}{8}\times \frac{1}{3} =\frac{1}{8}$

Hence probability of selecting Harry potter themed pants and Harry potter themed slippers is 1/8

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4 years ago

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